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| Главные авторы: | , |
|---|---|
| Формат: | Preprint |
| Опубликовано: |
2020
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| Предметы: | |
| Online-ссылка: | https://arxiv.org/abs/2010.00580 |
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Оглавление:
- The ball number of a link $L$, denoted by $ball(L)$, is the minimum number of solid balls (not necessarily of the same size) needed to realize a necklace representing $L$. In this paper, we show that $ball(L)\leq 5 cr(L)$ where $cr(L)$ denotes the crossing number of $L$. To this end, we use Lorentz geometry applied to ball packings. The well-known Koebe-Andreev-Thurston circle packing Theorem is also an important brick for the proof. Our approach yields to an algorithm to construct explicitly the desired necklace representation of $L$ in the 3-dimensional space.